Absorbing Powers of different Bodies for Light and Heat. 7 



tion last obtained, and which will afterwards be made use of, is 

 that openings 1 and 2 may be interchanged. 



§ 8. We shall now establish a law which may be regarded as 

 a generalization of that announced in the last section. 



Between the two black surfaces 1 and 2 of equal temperature, 

 imagine a body placed which may refract, reflect, and absorb 

 the rays which pass between them in any way whatever. Several 

 pencils may reach surface 2 from surface 1 ; of these let one be 

 chosen, and let that part of it be taken when it leaves 1, which 

 consists of waves of length between X and X-\- d\ and let this be 

 divided into two component parts polarized at right angles to 

 each other in the planes a x and b v Let that part of the first 

 component which reaches 2 be itself divided into two parts, 

 whose planes of polarization are the perpendicular but otherwise 

 arbitrary planes « 2 , 6 2 . Let the intensity of the part polarized 

 in # 2 be KdX. Of the pencil which pursues the same path, but 

 in the opposite direction, viz. from 2 to 1, consider at 2 the part 

 which consists of the waves whose length lies between X and 

 X + dX, and let it again be divided into two parts polarized in 

 the planes a q and b 2 , and let the portion of the first component 

 part that reaches 1 be also divided into two components polarized 

 in a x and b v Let the intensity of the part polarized in a x be K'dX. 

 Then K =K'. 



The truth of this proposition shall, in the first place, be esta- 

 blished on the hypothesis, first, that the rays suffer no diminu- 

 tion of intensity on their path, that is, that the refractions and 

 reflexions to which they may be subjected cause no loss, and 

 that there is no absorption; and secondly, that the rays that 

 proceed from 1 polarized in a v impinge on 2 polarized in « 2 , and 

 conversely. 



Through the middle point of 1 let a plane be placed perpen- 

 dicular to the axis of the incident and emerging pencil, and in 

 this plane let a system of rectangular coordinates be taken, of 

 which the middle point of 1 is the origin. Let x v y x be the coor- 

 dinates of some point in this plane (fig. 4). At the distance of 

 unity from this plane let another plane be taken pj g 4 



parallel to the first, and containing a system of 

 coordinates parallel to the first system, having 

 its origin in the axis of the pencil. Let # 3 , y 3 

 be the coordinates of a point in this plane. Simi- 

 larly, let a plane be taken passing through the 

 middle point of 2, perpendicular to the axis of 

 the incident and emerging pencil, and in this 

 plane let a system of rectangular coordinates be 

 taken having the middle point of 2 for its origin. 

 Let a? 2 , i/ 2 be the coordinates of a point in this 



